NCERT Exemplar Solutions
Class 12 - Mathematics - Chapter 1: RELATIONS AND FUNCTIONSFill in the Blanks
Class 12 - Mathematics - Chapter 1: RELATIONS AND FUNCTIONS
Question. 48
Let the relation \(R\) be defined in \(\mathbb{N}\) by \(aRb\) if \(2a + 3b = 30\). Then \(R = \) ____.
Answer:
\(\{(3,8),(6,6),(9,4),(12,2)\}\)
Question. 49
Let the relation \(R\) be defined on the set \(A=\{1,2,3,4,5\}\) by \(R=\{(a,b):|a^2-b^2|<8\}\). Then \(R\) is given by ____.
Answer:
\(\{(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3),(3,4),(4,3),(4,4),(5,5)\}\)
Question. 50
Let \(f=\{(1,2),(3,5),(4,1)\}\) and \(g=\{(2,3),(5,1),(1,3)\}\). Then \(g\circ f =\) ____ and \(f\circ g=\) ____.
Answer:
\(g\circ f=\{(1,3),(3,1),(4,3)\}\) and \(f\circ g=\{(2,5),(5,2),(1,5)\}\)
Question. 51
Let \(f:\mathbb{R}\to\mathbb{R}\) be defined by \(f(x)=\dfrac{x}{\sqrt{1+x^2}}\). Then \((f\circ f\circ f)(x)=\) ____.
Answer:
\(\dfrac{x}{\sqrt{3x^2+1}}\)
Question. 52
If \(f(x)=4-(x-7)^3\), then \(f^{-1}(x)=\) ____.
Answer:
\(7 + (4 - x)^{1/3}\)